Density: Concepts, Calculations, and Applications

Density

Concept of Density

Density is a fundamental property of matter that describes how much mass is contained in a given volume. It is commonly used in chemistry to compare substances and to solve problems involving mass and volume relationships.

• Definition: Density represents the amount of mass per unit of volume.

• Formula:

$\text{Density} = \frac{\text{mass}}{\text{volume}}$

• Units:

  • For solids and liquids: typically expressed in g/cm3 or g/mL

  • For gases: typically expressed in g/L

Example Calculation

To convert density from one unit to another, use dimensional analysis. For example, converting density from g/cm3 to lb/ft3:

• Given: Density of an unknown metal is 2.14 g/cm3. Express this density in lb/ft3.

• Conversion factors used:

  • 1 lb = 453.6 g

  • 1 in = 2.54 cm

  • 1 ft = 12 in

• Calculation steps:

  1. Convert g to lb: $2.14 \text{ g/cm}^3 \times \frac{1 \text{ lb}}{453.6 \text{ g}}$

  2. Convert cm3 to in3: $\times \left(\frac{2.54 \text{ cm}}{1 \text{ in}}\right)^3$

  3. Convert in3 to ft3: $\times \left(\frac{12 \text{ in}}{1 \text{ ft}}\right)^3$

• Final result: $133.6 \text{ lb/ft}^3$

Practice Application

Density is used in real-world applications such as determining the concentration of substances in solutions or mixtures. For example, assessing lead levels in blood:

• Problem: When lead levels in blood exceed 0.80 ppm (parts per million), the lead is considered dangerous. 0.80 ppm means that 1 million g of blood would contain 0.80 g of Pb. Given that the density of blood is 1.060 kg/L, how many grams of Pb would be found in 400.0 mL of blood at 0.80 ppm?

• Solution:

  • Convert 400.0 mL to g using the density of blood.

  • Calculate the mass of Pb using the ppm definition.

• Answer: 0.339 g Pb

Summary Table: Density Units and Conversions

State of Matter	Common Density Units	Conversion Factors
Solids/Liquids	g/cm3, g/mL	1 cm3 = 1 mL
Gases	g/L	1 L = 1000 mL
Imperial Units	lb/ft3	1 lb = 453.6 g; 1 ft = 12 in; 1 in = 2.54 cm

Additional info: Density is a key concept in chemistry, used to identify substances, calculate concentrations, and solve problems involving mixtures and solutions.